CHAPTER 5:Chemical Kinetics Copyright © 2020 by Nob Hill Publishing, LLC The purpose of this chapter is to provide a framework for determining the reaction rate given a detailed statement of the reaction chemistry. We use several concepts from the subject of chemical kinetics to illustrate two key points: 1 The stoichiometry of an elementary reaction defines the concentration dependence of the rate expression. 2 The quasi-steady-state assumption (QSSA) and the reaction equilibrium assumption allow us to generate reaction-rate expressions that capture the details of the reaction chemistry with a minimum number of rate constants. 1 / 152 The Concepts The concepts include: the elementary reaction Tolman's principle of microscopic reversibility elementary reaction kinetics the quasi-steady-state assumption the reaction equilibrium assumption The goals here are to develop a chemical kinetics basis for the empirical expression, and to show that kinetic analysis can be used to take mechanistic insight and describe reaction rates from first principles. 2 / 152 Reactions at Surfaces We also discuss heterogeneous catalytic adsorption and reaction kinetics. Catalysis has a significant impact on the United States economy1 and many important reactions employ catalysts.2 We demonstrate how the concepts for homogeneous reactions apply to heterogeneously catalyzed reactions with the added constraint of surface-site conservation. The physical characteristics of catalysts are discussed in Chapter 7. 1Catalysis is at the heart of the chemical industry, with sales in 1990 of $292 billion and employment of 1.1 million, and the petroleum refining industry, which had sales of $140 billion and employment of 0.75 million in 1990 [13]. 2Between 1930 and the 1980s, 63 major products and 34 major process innovations were introduced by the chemical industry. More than 60% of the products and 90% of these processes were based on catalysis[13]. 3 / 152 Elementary Reactions and Microscopic Reversibility Stoichiometric statements such as A + B )−*− C are used to represent the changes that occur during a chemical reaction. These statements can be interpreted in two ways. The reaction statement may represent the change in the relative amounts of species that is observed when the reaction proceeds. overall stoichiometry Or the reaction statement may represent the actual molecular events that are presumed to occur as the reaction proceeds. elementary reaction The elementary reaction is characterized by a change from reactants to products that proceeds without identifiable intermediate species forming. 4 / 152 Elementary Reactions and Rate Expressions For an elementary reaction, the reaction rates for the forward and reverse paths are proportional to the concentration of species taking part in the reaction raised to the absolute value of their stoichiometric coefficients. The reaction order in all species is determined directly from the stoichiometry. Elementary reactions are usually unimolecular or bimolecular because the probability of collision between several species is low and is not observed at appreciable rates. For an overall stoichiometry, on the other hand, any correspondence between the stoichiometric coefficients and the reaction order is purely coincidental. 5 / 152 Some Examples | Acetone decomposition The first example involves the mechanism proposed for the thermal decomposition of acetone at 900 K to ketene and methyl-ethyl ketone (2-butanone) [17]. The overall reaction can be represented by 3CH3COCH3 −! CO + 2CH4 + CH2CO + CH3COC2H5 6 / 152 Acetone decomposition The reaction is proposed to proceed by the following elementary reactions 3CH3COCH3 −! CO + 2CH4 + CH2CO + CH3COC2H5 CH3COCH3 −! CH3 + CH3CO CH3CO −! CH3 + CO CH3 + CH3COCH3 −! CH4 + CH3COCH2 CH3COCH2 −! CH2CO + CH3 CH3 + CH3COCH2 −! CH3COC2H5 7 / 152 Acetone decomposition The thermal decomposition of acetone generates four stable molecules that can be removed from the reaction vessel: CO, CH4, CH2CO and CH3COC2H5. Three radicals are formed and consumed during the thermal decomposition of acetone: CH3, CH3CO and CH3COCH2. These three radicals are reaction intermediates and cannot be isolated outside of the reaction vessel. 8 / 152 Overall stoichiometry from Mechanism Assign the species to the A vector as follows Species Formula Name A1 CH3COCH3 acetone A2 CH3 methyl radical A3 CH3CO acetyl radical A4 CO carbon monoxide A5 CH3COCH2 acetone radical A6 CH2CO ketene A7 CH4 methane A8 CH3COC2H5 methyl ethyl ketone The stoichiometric matrix is 2 −1 1 1 0 0 0 0 0 3 6 0 1 −1 1 0 0 0 0 7 6 7 ν = 6 −1 −1 0 0 1 0 1 0 7 6 7 4 0 1 0 0 −1 1 0 0 5 0 −1 0 0 −1 0 0 1 9 / 152 Overall stoichiometry from Mechanism Multiply ν by 1 1 2 1 1 We obtain −3 0 0 1 0 1 2 1 which is the overall stoichiometry given in Reaction 5.1. 10 / 152 Example Two | Smog The second example involves one of the major reactions responsible for the production of photochemical smog. The overall reaction and one possible mechanism are 2NO2 + hν −! 2NO + O2 NO2 + hν −! NO + O O + NO2 )−*− NO3 NO3 + NO2 −! NO + O2 + NO2 NO3 + NO −! 2NO2 O + NO2 −! NO + O2 11 / 152 Smog In this reaction mechanism, nitrogen dioxide is activated by absorbing photons and decomposes to nitric oxide and oxygen radicals (elementary Reaction 5.8). Stable molecules are formed: NO and O2 Radicals, O and NO3, are generated and consumed during the photochemical reaction. Work through the steps to determine the linear combination of the mechanistic steps that produces the overall reaction. 12 / 152 Example Three | Methane Synthesis The third example involves the synthesis of methane from synthesis gas, CO and H2, over a ruthenium catalyst [6]. The overall reaction and one possible mechanism are 3H2(g) + CO(g) −! CH4(g) + H2O(g) CO(g) + S )−*− COs COs + S )−*− Cs + Os Os + H2(g) −! H2O(g) + S H2(g) + 2S )−*− 2Hs Cs + Hs )−*− CHs + S CHs + Hs )−*− CH2s + S CH2s + Hs )−*− CH3s + S CH3s + Hs −! CH4(g) + 2S 13 / 152 Methane Synthesis The subscripts g and ads refer to gas phase and adsorbed species, respectively, and S refers to a vacant ruthenium surface site. During the overall reaction, the reagents adsorb (elementary Reactions 5.150 and 5.153), and the products form at the surface and desorb (elementary Reactions 5.152 and 5.157). Adsorbed CO (COs) either occupies surface sites or dissociates to adsorbed carbon and oxygen in elementary Reaction 5.151. 14 / 152 Methane Synthesis The adsorbed carbon undergoes a sequential hydrogenation to methyne, methylene, and methyl, all of which are adsorbed on the surface. Hydrogenation of methyl leads to methane in elementary Reaction 5.157. In this example, the overall reaction is twice the fourth reaction added to the remaining reactions. 15 / 152 Elementary Reactions | Characteristics One criterion for a reaction to be elementary is that as the reactants transform into the products they do so without forming intermediate species that are chemically identifiable. A second aspect of an elementary reaction is that the reverse reaction also must be possible on energy, symmetry and steric bases, using only the products of the elementary reaction. This reversible nature of elementary reactions is the essence of Tolman's principle of microscopic reversibility [19, p. 699]. 16 / 152 Microscopic Reversibility This assumption (at equilibrium the number of molecules going in unit time from state 1 to state 2 is equal to the number going in the reverse direction) should be recognized as a distinct postulate and might be called the principle of microscopic reversibility. In the case of a system in thermodynamic equilibrium, the principle requires not only that the total number of molecules leaving a given quantum state in unit time is equal to the number arriving in that state in unit time, but also that the number leaving by any one particular path, is equal to the number arriving by the reverse of that particular path. 17 / 152 Transition State Theory Various models or theories have been postulated to describe the rate of an elementary reaction. Transition state theory (TST)is reviewed briefly in the next section to describe the flow of systems (reactants −! products) over potential-energy surfaces. Using Tolman's principle, the most probable path in one direction must be the most probable path in the opposite direction. Furthermore, the Gibbs energy difference in the two directions must be equal to the overall Gibbs energy difference | the ratio of rate constants for an elementary reaction must be equal to the equilibrium constant for the elementary reaction. 18 / 152 Elementary Reaction Kinetics In this section we outline the transition-state theory (TST), which can be used to predict the rate of an elementary reaction. Our purpose is to show how the rate of an elementary reaction is related to the concentration of reactants. The result is Y −νij Y νij ri = ki cj − k−i cj (5.22) j2Ri j2Pi in which j 2 Ri and j 2 Pi represent the reactant species and the product species in the ith reaction, respectively. Equation 5.22 forms the basis for predicting reaction rates and is applied to homogeneous and heterogeneous systems. Because of its wide use, much of Chapter 5 describes the concepts and assumptions that underlie Equation 5.22. 19 / 152 Potential Energy Diagrams We consider a simple reaction to illustrate the ideas F + H H )−*− fF H Hg )−*− F H + H The potential energy V (r) of the molecule is related to the relative position of the atoms, and for a diatomic molecule the potential energy can be represented with a Morse function h i V (r) = D e−2βr − 2e−βr in which D is the dissociation energy, r is the displacement from the equilibrium bond length, and β is related to the vibrational frequency of the molecule. The following figure presents the Morse functions for HF and H2 molecules.